ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A,B and C. (The dotted lines are drawn additionally to help you).

Draw lines AD and DC such that AD||BC, AB||DC

AD = BC, AB = DC

ABCD is a rectangle as opposite sides are equal and parallel to each other and all the interior angles are of 90o

In a rectangle, diagonals are of equal length and also these bisect each other

Hence, AO = OC = BO = OD

Thus, O is equidistant from A, B, and C